Question

"Consider a cash flow for an investment project for years 0 through 5 given below: ($)
170
120
-540
-540
220
670
What is the i* for this cash flow? If the cash flow has multiple i*, please enter the minimum positive i*. Enter the i* as a percentage between 0 and 100."

Answer 1

Consider the given problem here all the cash flows are given in the question. Let’s assume that “i” be the rate of interest such that the “NPV” of all the cash flows will be “0”.

So, the NPV is given below.

=> 170 + 120/(1+i) + (-540) /(1+i)^2 + (-540) /(1+i)^3 + 220/(1+i)^4 + 670/(1+i)^5 = 0.

=> 170 + 120/(1+i) + 220/(1+i)^4 + 670/(1+i)^5 = 540/(1+i)^2 + 540/(1+i)^3.

Here we need to put different value of “i” and check for which value “NPV” is “0”. If we put “i=8%”.

=> NPV = 170 + 120/1.08 + (-540) /1.08^2 + (-540) /1.08^3 + 220/1.08^4 + 670/1.08^5 = 7.17 > 0.

Now at “i=9%” the NPV is given below.

=> NPV = 170 + 120/1.09 + (-540) /1.09^2 + (-540) /1.09^3 + 220/1.09^4 + 670/1.09^5 = (-0.08) < 0. So, at “i=9%”, the “NPV=(-0.08)” which is negative but very close to “zero”, => the required “i*=9%”.